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arXiv · 2103.00574

Random tree Besov priors -- Towards fractal imaging

Hanne Kekkonen·Matti Lassas·Eero Saksman·Samuli Siltanen
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Abstract

We propose alternatives to Bayesian a priori distributions that are frequently used in the study of inverse problems. Our aim is to construct priors that have similar good edge-preserving properties as total variation or Mumford-Shah priors but correspond to well defined infinite-dimensional random variables, and can be approximated by finite-dimensional random variables. We introduce a new wavelet-based model, where the non zero coefficient are chosen in a systematic way so that prior draws have certain fractal behaviour. We show that realisations of this new prior take values in some Besov spaces and have singularities only on a small set $\tau$ that has a certain Hausdorff dimension. We also introduce an efficient algorithm for calculating the MAP estimator, arising from the the new prior, in denoising problem.

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Hanne Kekkonen, Matti Lassas, Eero Saksman, Samuli Siltanen. 2021-02-28. Random tree Besov priors -- Towards fractal imaging. https://arxiv.org/abs/2103.00574

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